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C₂×#63020 #10586339

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

35160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

(1,2);(3,4)(5,8)(6,9)(7,10)(11,12,18,16)(13,19,15,14)(17,20,25,24)(21,26,23,22);(3,4)(5,8)(6,9)(7,10)(11,13,18,15)(12,14,16,19)(17,21,25,23)(20,22,24,26);(3,5)(4,7)(6,10)(8,9)(11,14)(12,15)(13,16)(17,22)(18,19)(20,23)(21,24)(25,26);(11,15,18,13)(12,19,16,14)(17,23,25,21)(20,26,24,22);(3,5)(4,8)(6,10)(7,9)(11,16,18,12)(13,19,15,14)(17,20,25,24)(21,22,23,26);(3,4)(5,7)(6,9)(8,10)(11,17)(12,20)(13,21)(14,22)(15,23)(16,24)(18,25)(19,26)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493535);